Function Norms
Definition: Function norms are norm definitions applied to function spaces. Function spaces are vector spaces whose elements are functions. The most common function spaces are Lp spaces.
V={f(.)∣f:[0,1]→Rs.t.∫01∣f(x)∣pdx<∞ 1≤p<∞}
We can define norms on V as follows:
∥f∥p:=(∫01∣f(x)∣pdx)1/p
where p≥1.
Specific Cases
- ∥f∥1=∫01∣f(x)∣dx L1−norm
- ∥f∥2=(∫01∣f(x)∣2dx)1/2 L2−norm
- ∥f∥∞=supx∈[0,1]∣f(x)∣ L∞−norm
#EE501 - Linear Systems Theory at METU